Lecture on Discounted Cash Flow: Capital Rationing

Introduction

• Lecture based on Chapter 9 of Open Tuition free lecture notes
• Focus on three situations in discounted cash flow: Capital Rationing, Replacement, Lease vs. Buy
• Each situation has its own technique and separate lecture

Capital Rationing

• Definition: Limited amount of capital available for investment
• Example Projects: A, B, C, D with their respective cash flows and NPVs calculated at 10% cost of capital
• If no capital rationing, accept all projects with positive NPV
• Capital Limitation: Only $1,600 available, but $1,800 needed for all projects

Problem Approach

• Projects Infinitely Divisible: Can invest any fraction of a project
  • Example: Investing 50% in a project results in 50% outflows and inflows
• NPV Per Dollar Invested:
  • Calculate NPV per dollar invested for each project
  • Prioritize projects based on highest NPV per dollar

Calculating NPV Per Dollar

• Project D: $50 NPV / $400 = $0.125 per dollar
• Project C: $36 NPV / $300 = $0.12 per dollar
• Project A: $50 NPV / $500 = $0.10 per dollar
• Project B: $57 NPV / $600 = $0.095 per dollar

Investment Strategy

• Invest in projects in order of highest NPV per dollar
• Maximum investment possible in each project:
  • Invest full in D, C, and part of A
  • Remaining funds into B up to available capital
• Total Maximum NPV Achieved: $174

Projects Not Infinitely Divisible

• New Scenario: Projects can't be fractioned, full 100% or none
• Evaluate all possible combinations of projects
• Combinations:
  • A, B, C; A, C, D; A, B, D; B, C, D
• Optimal Combination: A, B, D with total NPV of $157

Handling Remaining Capital

• If capital remains unused, don't borrow more than needed
• Unused funds should be returned or not borrowed

Capital Rationing Reasons

• Hard Capital Rationing: Lenders refuse to lend more
• Soft Capital Rationing: Self-imposed limit by the company
  • Similar to personal borrowing decisions

Conclusion

• Discussed capital rationing as a part of discounted cash flow
• Upcoming Lecture: Replacement